Ultrametric research has emerged as a major department of arithmetic lately. This publication offers, for the 1st time, a quick survey of the learn up to now in ultrametric summability conception, that is a fusion of a classical department of arithmetic (summability thought) with a latest department of study (ultrametric analysis). numerous mathematicians have contributed to summability conception in addition to practical research. The e-book will attract either younger researchers and more matured mathematicians who're trying to discover new parts in analysis.

The research of mathematics differential operators is a singular and promising region of arithmetic. this whole creation to the topic starts off with the fundamentals: a dialogue of p-adic numbers and a few of the classical differential research at the box of p-adic numbers resulting in the definition of mathematics differential operators in this box.

This is often an advent to p-adic research that is trouble-free but whole and which screens the diversity of functions of the topic. Dr Schikhof is ready to indicate and clarify how p-adic and 'real' research vary. This technique promises the reader fast turns into accustomed to this both 'real' research and appreciates its relevance.

Illustration thought of huge teams is a crucial and speedy constructing a part of glossy arithmetic, giving upward push to numerous very important functions in likelihood and mathematical physics. This booklet offers the 1st concise and self-contained creation to the idea at the least difficult but very nontrivial instance of the countless symmetric crew, concentrating on its deep connections to chance, mathematical physics, and algebraic combinatorics.